You know, anything that has time travel has to use some sort of artificial restrictions, so I won't begrudge them that. I am a huge fan of the Back to the Future series, but they continually used various gimmicks. For example, if Marty had given himself more than 10 minutes of time to help future Doc in the first movie, the climax would have been uninteresting. Then you have a time machine that is constantly malfunctioning or unavailable, and you have characters acting as if they couldn't simply fail once, then go back in time and fix that if they really needed to -- as if they only had one shot at getting the Almanac back, or whatever.
There is one particular scene in the second movie where Marty stands on the edge of the building, considering jumping off, where Biff is about to shoot him. Then Doc shows up (unseen), and Marty jumps off onto the Delorean. How did Doc know to show up there? This seems on the surface to be yet another of the coincidences that the movie trades in so heavily, but I like to imagine it differently (and this fits): Doc knew where to show up because Marty died, Doc saw this in the future, and then came back to rescue him. I find that much more compelling.
Anyway, my point is that of course the time travel is a gimmick in some way. Pure, unfettered time travel is far too powerful to make for an interesting narrative, let alone an interesting game. What will be the deciding factor for this game, or any other piece of entertainment featuring time travel, is if the gimmick is fun and interesting, and if it survives the suspension of disbelief to a certain extent.
Yeah, this was a big tangent...